The lifespans of porcupines in a particular zoo are normally distributed. The average porcupine lives $21$ years; the standard deviation is $1.6$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a porcupine living between $22.6$ and $24.2$ years.
Explanation: $21$ $19.4$ $22.6$ $17.8$ $24.2$ $16.2$ $25.8$ $95\%$ $68\%$ $13.5\%$ $13.5\%$ We know the lifespans are normally distributed with an average lifespan of $21$ years. We know the standard deviation is $1.6$ years, so one standard deviation below the mean is $19.4$ years and one standard deviation above the mean is $22.6$ years. Two standard deviations below the mean is $17.8$ years and two standard deviations above the mean is $24.2$ years. Three standard deviations below the mean is $16.2$ years and three standard deviations above the mean is $25.8$ years. We are interested in the probability of a porcupine living between $22.6$ and $24.2$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the porcupines will have lifespans within 2 standard deviations of the average lifespan. It also tells us that $68\%$ of the porcupines will have lifespans within 1 standard deviation of the mean. The probability of a particular porcupine living between $22.6$ and $24.2$ years is $\color{orange}{13.5\%}$.